Regression trees example 1
1 Preparations
Load the necessary libraries
2 Scenario
Loyn (1987) modelled the abundance of forest birds with six predictor variables (patch area, distance to nearest patch, distance to nearest larger patch, grazing intensity, altitude and years since the patch had been isolated).
| ABUND | DIST | LDIST | AREA | GRAZE | ALT | YR.ISOL |
|---|---|---|---|---|---|---|
| .. | .. | .. | .. | .. | .. | .. |
| ABUND | Abundance of forest birds in patch- response variable |
| DIST | Distance to nearest patch - predictor variable |
| LDIST | Distance to nearest larger patch - predictor variable |
| AREA | Size of the patch - predictor variable |
| GRAZE | Grazing intensity (1 to 5, representing light to heavy) - predictor variable |
| ALT | Altitude - predictor variable |
| YR.ISOL | Number of years since the patch was isolated - predictor variable |
The aim of the analysis is to investigate the effects of a range of predictors on the abundance of forest birds.
We have previously analysed these data in Example 4 and the Bayesian version (Example 4). On those occasions, we used a multiple linear model with scaled predictors (some of which were also log-transformed) against a lognormal distribution.
On this occassion we will take a different approach. We will use regression trees in order to explore which variables might be “important” drivers of bird abundances and the possible nature of any relationships and interactions. Such an analysis might help refine sensible candidate models to explore via linear modelling, yet might also serve as either an analysis in its own right
3 Read in the data
Rows: 56 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (7): ABUND, AREA, YR.ISOL, DIST, LDIST, GRAZE, ALT
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Rows: 56
Columns: 7
$ ABUND <dbl> 5.3, 2.0, 1.5, 17.1, 13.8, 14.1, 3.8, 2.2, 3.3, 3.0, 27.6, 1.8…
$ AREA <dbl> 0.1, 0.5, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.…
$ YR.ISOL <dbl> 1968, 1920, 1900, 1966, 1918, 1965, 1955, 1920, 1965, 1900, 19…
$ DIST <dbl> 39, 234, 104, 66, 246, 234, 467, 284, 156, 311, 66, 93, 39, 40…
$ LDIST <dbl> 39, 234, 311, 66, 246, 285, 467, 1829, 156, 571, 332, 93, 39, …
$ GRAZE <dbl> 2, 5, 5, 3, 5, 3, 5, 5, 4, 5, 3, 5, 2, 1, 5, 5, 3, 3, 3, 2, 2,…
$ ALT <dbl> 160, 60, 140, 160, 140, 130, 90, 60, 130, 130, 210, 160, 210, …Rows: 56
Columns: 7
$ ABUND <dbl> 5.3, 2.0, 1.5, 17.1, 13.8, 14.1, 3.8, 2.2, 3.3, 3.0, 27.6, 1.8…
$ AREA <dbl> 0.1, 0.5, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.…
$ YR.ISOL <dbl> 1968, 1920, 1900, 1966, 1918, 1965, 1955, 1920, 1965, 1900, 19…
$ DIST <dbl> 39, 234, 104, 66, 246, 234, 467, 284, 156, 311, 66, 93, 39, 40…
$ LDIST <dbl> 39, 234, 311, 66, 246, 285, 467, 1829, 156, 571, 332, 93, 39, …
$ GRAZE <dbl> 2, 5, 5, 3, 5, 3, 5, 5, 4, 5, 3, 5, 2, 1, 5, 5, 3, 3, 3, 2, 2,…
$ ALT <dbl> 160, 60, 140, 160, 140, 130, 90, 60, 130, 130, 210, 160, 210, …# A tibble: 6 × 7
ABUND AREA YR.ISOL DIST LDIST GRAZE ALT
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 5.3 0.1 1968 39 39 2 160
2 2 0.5 1920 234 234 5 60
3 1.5 0.5 1900 104 311 5 140
4 17.1 1 1966 66 66 3 160
5 13.8 1 1918 246 246 5 140
6 14.1 1 1965 234 285 3 130spc_tbl_ [56 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
$ ABUND : num [1:56] 5.3 2 1.5 17.1 13.8 14.1 3.8 2.2 3.3 3 ...
$ AREA : num [1:56] 0.1 0.5 0.5 1 1 1 1 1 1 1 ...
$ YR.ISOL: num [1:56] 1968 1920 1900 1966 1918 ...
$ DIST : num [1:56] 39 234 104 66 246 234 467 284 156 311 ...
$ LDIST : num [1:56] 39 234 311 66 246 ...
$ GRAZE : num [1:56] 2 5 5 3 5 3 5 5 4 5 ...
$ ALT : num [1:56] 160 60 140 160 140 130 90 60 130 130 ...
- attr(*, "spec")=
.. cols(
.. ABUND = col_double(),
.. AREA = col_double(),
.. YR.ISOL = col_double(),
.. DIST = col_double(),
.. LDIST = col_double(),
.. GRAZE = col_double(),
.. ALT = col_double()
.. )
- attr(*, "problems")=<externalptr> loyn (56 rows and 7 variables, 7 shown)
ID | Name | Type | Missings | Values | N
---+---------+---------+----------+--------------+-----------
1 | ABUND | numeric | 0 (0.0%) | [1.5, 39.6] | 56
---+---------+---------+----------+--------------+-----------
2 | AREA | numeric | 0 (0.0%) | [0.1, 1771] | 56
---+---------+---------+----------+--------------+-----------
3 | YR.ISOL | numeric | 0 (0.0%) | [1890, 1976] | 56
---+---------+---------+----------+--------------+-----------
4 | DIST | numeric | 0 (0.0%) | [26, 1427] | 56
---+---------+---------+----------+--------------+-----------
5 | LDIST | numeric | 0 (0.0%) | [26, 4426] | 56
---+---------+---------+----------+--------------+-----------
6 | GRAZE | numeric | 0 (0.0%) | 1 | 13 (23.2%)
| | | | 2 | 8 (14.3%)
| | | | 3 | 15 (26.8%)
| | | | 4 | 7 (12.5%)
| | | | 5 | 13 (23.2%)
---+---------+---------+----------+--------------+-----------
7 | ALT | numeric | 0 (0.0%) | [60, 260] | 56
-------------------------------------------------------------4 Exploratory data analysis
The GRAZE predictor represents grazing intensity. Note, this was essentially a categorical variable with levels 1 (no grazing) through to 5 (intense grazing). Although we could attempt to model this as a continuous predictor, such an approach would assume that this is a linear scale in which the interval between each successive level is the same. That is, the difference between level 1 and 2 is the same as the difference between 4 and 5 etc. Since, these were categories, such spacing is not guaranteed. It might therefore be better to model this variable as a categorical variable.
Finally, even in the absence of issues relating to the range of each predictor within each level of GRAZE, it might still be advantageous to centre each predictor. Centering will provide computational advantages and also ensure that the intercept has a more useful meaning.
Unlike linear models, regression trees make fewer assumptions about the data. For example, normality (distribution), homogeneity of variable (dispersion) and linearity are no longer assumed. Rather than optimising against a likelihood, regression trees use a loss function.
Nevertheless, it is always insightful to explore the data prior to performing any analyses.
For regression trees, it is also important to consider whether you want to impose monotonic relationships. Monotonic relationships are those that only advance either positively or negatively. Regression trees are inherently non-linear and have the tendency to overfit to minor perturbations in the training data. In situations where such undulations would lack ecological reasoning, we can specify that a specific partial trend must be monotonic.
A scatterplot matrix plots each variable against each other. It is useful to provide boxplots in the diagonals to help explore the distributions.
scatterplotMatrix(~ ABUND + DIST + LDIST + AREA + fGRAZE + ALT + YR.ISOL,
data = loyn,
diagonal = list(method = "boxplot")
)
Conclusions:
- on the top row, ABUND is on the y-axis of each plot
- the second plot from the top left has DIST on the x-axis
- it is clear from looking at the boxplots on the diagonals that some of the potential predictors (DIST, LDIST and AREA) are not normally distributed.
- it might be worth log-transforming these variables. Not only might this help normalise those predictors, it might also improve the linearity between the response and those predictors.
- we will reserve all other judgements of assumptions until we explore these log-transformations
5 Fit the model
We will now determine the optimum number of trees estimated to be required in order to achieve a balance between bias (biased towards the exact observations) and precision (variability in estimates). Ideally, the optimum number of trees should be close to 1000. If it is much less (as in this case), it could imply that the tree learned too quickly. On the other hand, if the optimum number of trees is very close to the total number of fitted trees, then it suggests that the optimum may not actually have occured yet and that more trees should be used (or a faster learning rate).
OOB generally underestimates the optimal number of iterations although predictive performance is reasonably competitive. Using cv_folds>1 when calling gbm usually results in improved predictive performance.
[1] 218
attr(,"smoother")
Call:
loess(formula = object$oobag.improve ~ x, enp.target = min(max(4,
length(x)/10), 50))
Number of Observations: 10000
Equivalent Number of Parameters: 39.99
Residual Standard Error: 0.04646 
[1] 315Conclusions:
- both out-of-bag and cross validation suggest that the total number of trees greatly exceeds the number necessary to achieve the optimum balance between bias and precision.
- the best iterations for either method is less than 1000 suggesting that the learning rate was too fast
- it might be worth decreasing the learning rate.
- we can probably also reduce the total number of trees (so that it runs a little quicker)
OOB generally underestimates the optimal number of iterations although predictive performance is reasonably competitive. Using cv_folds>1 when calling gbm usually results in improved predictive performance.
[1] 1568
attr(,"smoother")
Call:
loess(formula = object$oobag.improve ~ x, enp.target = min(max(4,
length(x)/10), 50))
Number of Observations: 5000
Equivalent Number of Parameters: 39.99
Residual Standard Error: 0.008792 
[1] 2218Conclusions:
- that is better
6 Explore relative influence
If a predictor is an important driver of the patterns in the response, then many of the tree splits should feature this predictor. It thus follows that the number of proportion of total splits that features each predictor will be a measure of the relative influence of each of the predictors.
var rel.inf
AREA AREA 46.375610
fGRAZE fGRAZE 28.433800
DIST DIST 9.033234
ALT ALT 6.303497
LDIST LDIST 6.275288
YR.ISOL YR.ISOL 3.578571Conclusions:
- shell weight is overwelmingly the most influential predictor.
- we can also ascribe a kind of signficance to the influence values by determining which of them are greater than \(100/p\) where \(p\) is the number of predictors. The logic here is that if all predictors were equally influential, then they would all have a relative influence of \(100/p\). Hence, any predictors that have a relative influence greater than this number must be explaining more than its share (and more than pure chance) and predictors with relative influence lower are explaining less than chance (and therefore not significantly influential).
7 Explore partial effects
[1] "DIST" "LDIST" "AREA" "fGRAZE" "ALT" "YR.ISOL"
loyn.gbm |>
pdp::partial(
pred.var = "AREA",
n.trees = best.iter,
recursive = FALSE,
inv.link = I
) |>
autoplot()
loyn.gbm |>
pdp::partial(
pred.var = "AREA",
n.trees = best.iter,
recursive = FALSE,
inv.link = I
) |>
autoplot() +
scale_x_log10()
Lets use a log x scale so that we can have greater granularity over the small patch areas. To do this, it is best to also create a custom prediction grid that is evenly spaced on the log scale.
newdata <- with(loyn, data.frame(lAREA = seq(min(log(AREA)), max(log(AREA)), len = 100))) |>
mutate(AREA = exp(lAREA)) |>
dplyr::select(-lAREA)
loyn.gbm |>
pdp::partial(
pred.var = "AREA",
pred.grid = newdata,
n.trees = best.iter,
recursive = FALSE,
inv.link = I
) |>
autoplot() +
scale_x_log10()
Recursive indicates that a weighted tree traversal method described by Friedman 2001 (which is very fast) should be used (only works for gbm). Otherwise a slower brute force method is used. If want to back transform - need to use brute force.
nms <- attr(loyn.gbm$Terms, "term.labels")
p <- vector("list", length(nms))
names(p) <- nms
for (nm in nms) {
print(nm)
p[[nm]] <- loyn.gbm |>
pdp::partial(
pred.var = nm,
n.trees = best.iter,
inv.link = I,
recursive = FALSE,
type = "regression"
) |>
autoplot() + ylim(0, 30)
}[1] "DIST"
[1] "LDIST"
[1] "AREA"
[1] "fGRAZE"
[1] "ALT"
[1] "YR.ISOL"
pp <- map(
.x = nms,
.f = ~
loyn.gbm |>
pdp::partial(
pred.var = .x,
n.trees = best.iter,
inv.link = I,
recursive = FALSE,
type = "regression"
) |>
autoplot() + ylim(0, 30)
)
patchwork::wrap_plots(pp) & theme_classic()
We might also want to explore interactions…
newdata <- with(
loyn,
expand.grid(
lAREA = seq(min(log(AREA)), max(log(AREA)), len = 100),
fGRAZE = levels(fGRAZE)
)
) |>
mutate(
AREA = exp(lAREA),
fGRAZE = factor(fGRAZE)
) |>
dplyr::select(AREA, fGRAZE)
head(newdata) AREA fGRAZE
1 0.1000000 1
2 0.1103853 1
3 0.1218492 1
4 0.1345036 1
5 0.1484722 1
6 0.1638915 1pdp::partial(loyn.gbm,
pred.var = c("AREA", "fGRAZE"),
pred.grid = newdata,
n.trees = best.iter,
recursive = TRUE
) |>
autoplot() +
scale_x_log10()
## g1 = loyn.gbm %>% pdp::partial(pred.var='SHELL_WEIGHT', n.trees=best.iter,
## recursive=FALSE,inv.link=exp) %>%
## autoplot
## g2 = loyn.gbm %>% pdp::partial(pred.var='HEIGHT', n.trees=best.iter,
## recursive=FALSE,inv.link=exp) %>%
## autoplot
## g1 + g2
newdata <- with(
loyn,
expand.grid(
lAREA = seq(min(log(AREA)), max(log(AREA)), len = 100),
fGRAZE = levels(fGRAZE),
DIST = NA, LDIST = NA, ALT = NA, YR.ISOL = NA
)
) |>
mutate(
AREA = exp(lAREA),
fGRAZE = factor(fGRAZE)
) |>
dplyr::select(DIST, LDIST, AREA, fGRAZE, ALT, YR.ISOL)
loyn.fit <- newdata |>
mutate(fit = predict(loyn.gbm,
newdata = newdata,
n.trees = best.iter
))
loyn.fit |>
ggplot(aes(y = fit, x = AREA, colour = fGRAZE)) +
geom_line() +
scale_x_log10()
The following no longer works
loyn.fit <-
pdp::partial(loyn.gbm,
pred.var = c("AREA", "fGRAZE"),
pred.grid = newdata,
n.trees = best.iter,
recursive = TRUE
) |>
as.data.frame()
head(loyn.fit) AREA fGRAZE yhat NA NA NA NA
1 NA NA 0.1000000 1 NA NA 18.75019
2 NA NA 0.1000000 2 NA NA 18.75019
3 NA NA 0.1000000 3 NA NA 18.75019
4 NA NA 0.1000000 4 NA NA 18.75019
5 NA NA 0.1000000 5 NA NA 18.75019
6 NA NA 0.1103853 1 NA NA 18.75019loyn.fit |> ggplot(aes(y = yhat, x = AREA)) +
geom_line(aes(colour = fGRAZE)) +
scale_x_log10() +
theme_classic()Warning: Removed 500 rows containing missing values or values outside the scale range
(`geom_line()`).
8 Explore interactions
What were the strong main effects:
- AREA
- fGRAZE
- YR.ISOL
- ALT
terms <- attr(loyn.gbm$Terms, "term.labels")
loyn.int <- NULL
for (i in 1:(length(terms) - 1)) {
for (j in (i + 1):length(terms)) {
print(paste("i=", i, " Name = ", terms[i]))
print(paste("j=", j, " Name = ", terms[j]))
loyn.int <- rbind(
loyn.int,
data.frame(
Var1 = terms[i], Var2 = terms[j],
"H.stat" = interact.gbm(loyn.gbm, loyn, c(i, j),
n.tree = best.iter
)
)
)
}
}[1] "i= 1 Name = DIST"
[1] "j= 2 Name = LDIST"
[1] "i= 1 Name = DIST"
[1] "j= 3 Name = AREA"
[1] "i= 1 Name = DIST"
[1] "j= 4 Name = fGRAZE"
[1] "i= 1 Name = DIST"
[1] "j= 5 Name = ALT"
[1] "i= 1 Name = DIST"
[1] "j= 6 Name = YR.ISOL"
[1] "i= 2 Name = LDIST"
[1] "j= 3 Name = AREA"
[1] "i= 2 Name = LDIST"
[1] "j= 4 Name = fGRAZE"
[1] "i= 2 Name = LDIST"
[1] "j= 5 Name = ALT"
[1] "i= 2 Name = LDIST"
[1] "j= 6 Name = YR.ISOL"
[1] "i= 3 Name = AREA"
[1] "j= 4 Name = fGRAZE"
[1] "i= 3 Name = AREA"
[1] "j= 5 Name = ALT"
[1] "i= 3 Name = AREA"
[1] "j= 6 Name = YR.ISOL"
[1] "i= 4 Name = fGRAZE"
[1] "j= 5 Name = ALT"
[1] "i= 4 Name = fGRAZE"
[1] "j= 6 Name = YR.ISOL"
[1] "i= 5 Name = ALT"
[1] "j= 6 Name = YR.ISOL" Var1 Var2 H.stat
1 AREA fGRAZE 0.24293603
2 DIST LDIST 0.13960598
3 DIST fGRAZE 0.12926350
4 fGRAZE ALT 0.07922100
5 DIST ALT 0.07402979
6 AREA ALT 0.07322587
7 DIST YR.ISOL 0.05117146
8 DIST AREA 0.04990394
9 LDIST fGRAZE 0.04947903
10 fGRAZE YR.ISOL 0.04737633
11 LDIST YR.ISOL 0.04593770
12 LDIST ALT 0.04385418
13 LDIST AREA 0.03812351
14 ALT YR.ISOL 0.02929411
15 AREA YR.ISOL 0.023597239 Tuning
The takes a long time - do over a break
# A tibble: 6 × 8
ABUND AREA YR.ISOL DIST LDIST GRAZE ALT fGRAZE
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <fct>
1 5.3 0.1 1968 39 39 2 160 2
2 2 0.5 1920 234 234 5 60 5
3 1.5 0.5 1900 104 311 5 140 5
4 17.1 1 1966 66 66 3 160 3
5 13.8 1 1918 246 246 5 140 5
6 14.1 1 1965 234 285 3 130 3 set.seed(123)
loyn.gbm1 <- gbm.step(
data = loyn |> as.data.frame(),
gbm.x = c(2:5, 7, 8),
gbm.y = 1,
tree.complexity = 7,
var.monotone = c(1, 1, 1, 1, 1, 0),
learning.rate = 0.001,
bag.fraction = 0.5,
family = "gaussian",
n.trees = 1000,
step.size = 1000,
max.trees = 10000
)
GBM STEP - version 2.9
Performing cross-validation optimisation of a boosted regression tree model
for ABUND and using a family of gaussian
Using 56 observations and 6 predictors
creating 10 initial models of 1000 trees
folds are unstratified
total mean deviance = 113.1773
tolerance is fixed at 0.1132
ntrees resid. dev.
1000 70.0734
now adding trees...
2000 52.6438
3000 45.6783
4000 42.8919
5000 42.2368
6000 42.3832
7000 42.8948
8000 43.3697
9000 44.0321
10000 44.5394 
fitting final gbm model with a fixed number of 5000 trees for ABUND
mean total deviance = 113.177
mean residual deviance = 26.588
estimated cv deviance = 42.237 ; se = 6.163
training data correlation = 0.876
cv correlation = 0.78 ; se = 0.041
elapsed time - 0.03 minutes
########### warning ##########
maximum tree limit reached - results may not be optimal
- refit with faster learning rate or increase maximum number of trees 
var rel.inf
AREA AREA 51.3441970
fGRAZE fGRAZE 36.0758288
ALT ALT 9.0416938
YR.ISOL YR.ISOL 2.1921059
LDIST LDIST 0.8012732
DIST DIST 0.5449014Warning in gbm.plot(loyn.gbm1, n.plots = 7, write.title = FALSE): reducing no
of plotted predictors to maximum available (6)
gbm.interactions - version 2.9
Cross tabulating interactions for gbm model with 6 predictors1 2 3 4 5 Length Class Mode
rank.list 5 data.frame list
interactions 36 -none- numeric
gbm.call 21 -none- list var1.index var1.names var2.index var2.names int.size
1 7 <NA> 0 0
2 6 fGRAZE 5 ALT 0maximum value = 26.45
10 Bootstrapping
nBoot <- 10
loyn.pred <- with(
loyn,
expand.grid(
lAREA = seq(min(log(AREA)), max(log(AREA)), len = 100),
fGRAZE = levels(fGRAZE),
DIST = NA,
LDIST = NA,
ALT = NA,
YR.ISOL = NA
)
) |>
mutate(
fGRAZE = factor(fGRAZE),
AREA = exp(lAREA)
) |>
dplyr::select(AREA, lAREA, fGRAZE, DIST, LDIST, ALT, YR.ISOL)
loyn.list <- vector("list", nBoot)
## loyn.list
loyn.sum <- vector("list", nBoot)
for (i in 1:nBoot) {
print(paste0("Boot number: ", i))
## Create random set
loyn.rnd <- loyn |>
sample_n(size = n(), replace = TRUE)
## Fit the trees
loyn.gbm <- gbm(ABUND ~ AREA + fGRAZE + DIST + LDIST + ALT + YR.ISOL,
data = loyn.rnd,
distribution = "gaussian",
var.monotone = c(1, 0, 1, 1, 1, 1),
n.trees = 5000,
interaction.depth = 7,
bag.fraction = 0.5,
shrinkage = 0.001,
train.fraction = 1,
n.minobsinnode = 2,
cv.folds = 3
)
## Determine the best number of trees
(best.iter <- gbm.perf(loyn.gbm, method = "cv"))
## predict based on shell weight
fit <- predict(loyn.gbm, newdata = loyn.pred, n.trees = best.iter)
loyn.list[[i]] <- data.frame(loyn.pred, Boot = i, Fit = fit)
## relative influence
loyn.sum[[i]] <- summary(loyn.gbm, n.trees = best.iter)
}[1] "Boot number: 1"
[1] "Boot number: 2"
[1] "Boot number: 3"
[1] "Boot number: 4"
[1] "Boot number: 5"
[1] "Boot number: 6"
[1] "Boot number: 7"
[1] "Boot number: 8"
[1] "Boot number: 9"
[1] "Boot number: 10"
loyn.fit <- do.call("rbind", loyn.list)
loyn.fit <- loyn.fit |>
group_by(AREA, fGRAZE) |>
## summarise(Median = median(Fit),
## Lower = quantile(Fit, p=0.025),
## Upper = quantile(Fit, p=0.975))
ggdist::median_hdci(Fit)
g1 <- loyn.fit |> ggplot(aes(y = Fit, x = AREA, fill = fGRAZE, color = fGRAZE)) +
geom_ribbon(aes(ymin = .lower, ymax = .upper), alpha = 0.3, color = NA) +
geom_line() +
scale_fill_viridis_d() +
scale_colour_viridis_d() +
scale_x_log10() +
theme_classic()
loyn.inf <- do.call("rbind", loyn.sum)
loyn.inf <- loyn.inf |>
group_by(var) |>
ggdist::median_hdci(rel.inf)
g2 <- loyn.inf |>
arrange(rel.inf) |>
mutate(var = factor(var, levels = unique(var))) |>
ggplot(aes(y = var, x = rel.inf)) +
geom_vline(xintercept = 12.5, linetype = "dashed") +
geom_pointrange(aes(xmin = .lower, xmax = .upper)) +
theme_classic()
g2 + patchwork::inset_element(g1, left = 0.3, bottom = 0.01, right = 1, top = 0.7)
set.seed(123)
nBoot <- 10
loyn.boot <-
tibble(Boot = 1:nBoot) |>
## Create bootstrapp data sets
mutate(data = map(
.x = Boot,
.f = ~ loyn |>
sample_n(size = n(), replace = TRUE)
)) |>
## Fit the trees
mutate(gbm = map2(
.x = data,
.y = Boot,
.f = ~ {
print(paste("Boot=", .y))
loyn.gbm <- gbm(ABUND ~ AREA + fGRAZE + DIST + LDIST + ALT + YR.ISOL,
data = .x,
distribution = "gaussian",
var.monotone = c(1, 0, 1, 1, 1, 1),
n.trees = 5000,
interaction.depth = 7,
bag.fraction = 0.5,
shrinkage = 0.001,
train.fraction = 1,
n.minobsinnode = 2,
cv.folds = 3
)
}
)) |>
## Determine the best number of trees
mutate(best.iter = map(
.x = gbm,
.f = ~ gbm.perf(.x, method = "cv")
)) |>
## predict
mutate(fit = map2(
.x = gbm,
.y = best.iter,
.f = ~ newdata |>
mutate(fit = predict(.x, newdata = loyn.pred, n.trees = .y))
)) |>
## relative influence
mutate(infl = map2(
.x = gbm,
.y = best.iter,
.f = ~ summary(.x, n.trees = .y)
))[1] "Boot= 1"
[1] "Boot= 2"
[1] "Boot= 3"
[1] "Boot= 4"
[1] "Boot= 5"
[1] "Boot= 6"
[1] "Boot= 7"
[1] "Boot= 8"
[1] "Boot= 9"
[1] "Boot= 10"
# A tibble: 56 × 8
ABUND AREA YR.ISOL DIST LDIST GRAZE ALT fGRAZE
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <fct>
1 6.8 10 1962 337 519 3 110 3
2 8 2 1900 259 259 5 120 5
3 34.4 96 1976 39 519 2 175 2
4 14.6 2 1972 402 402 1 210 1
5 1.5 0.5 1900 104 311 5 140 5
6 24.9 29 1965 545 770 3 130 3
7 31 57 1963 467 467 1 165 1
8 33 144 1940 146 319 1 190 1
9 29 32 1974 208 208 1 190 1
10 11.5 17 1920 389 2595 5 100 5
# ℹ 46 more rows# A tibble: 56 × 8
ABUND AREA YR.ISOL DIST LDIST GRAZE ALT fGRAZE
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <fct>
1 2.2 1 1920 284 1829 5 60 5
2 1.8 2 1890 93 93 5 160 5
3 21.2 2 1973 39 39 2 210 2
4 2.9 3 1965 26 26 3 140 3
5 27.8 12 1963 159 159 4 110 4
6 16.3 7 1965 285 882 3 130 3
7 19.5 6 1890 93 226 3 170 3
8 26 18 1966 40 3188 2 190 2
9 24.4 4 1973 234 519 2 220 2
10 8 2 1900 259 259 5 120 5
# ℹ 46 more rows DIST LDIST AREA fGRAZE ALT YR.ISOL fit
1 NA NA 0.1000000 1 NA NA 9.390859
2 NA NA 0.1103853 1 NA NA 9.390859
3 NA NA 0.1218492 1 NA NA 9.390859
4 NA NA 0.1345036 1 NA NA 9.390859
5 NA NA 0.1484722 1 NA NA 9.390859
6 NA NA 0.1638915 1 NA NA 9.390859
7 NA NA 0.1809122 1 NA NA 9.390859
8 NA NA 0.1997005 1 NA NA 9.390859
9 NA NA 0.2204400 1 NA NA 9.390859
10 NA NA 0.2433334 1 NA NA 9.390859
11 NA NA 0.2686043 1 NA NA 9.390859
12 NA NA 0.2964997 1 NA NA 9.390859
13 NA NA 0.3272921 1 NA NA 9.390859
14 NA NA 0.3612825 1 NA NA 9.390859
15 NA NA 0.3988028 1 NA NA 9.390859
16 NA NA 0.4402197 1 NA NA 9.390859
17 NA NA 0.4859379 1 NA NA 9.390859
18 NA NA 0.5364041 1 NA NA 9.390859
19 NA NA 0.5921113 1 NA NA 9.390859
20 NA NA 0.6536040 1 NA NA 9.390859
21 NA NA 0.7214828 1 NA NA 9.390859
22 NA NA 0.7964110 1 NA NA 9.390859
23 NA NA 0.8791208 1 NA NA 9.390859
24 NA NA 0.9704203 1 NA NA 9.390859
25 NA NA 1.0712015 1 NA NA 9.390859
26 NA NA 1.1824491 1 NA NA 9.390859
27 NA NA 1.3052502 1 NA NA 9.390859
28 NA NA 1.4408045 1 NA NA 9.390859
29 NA NA 1.5904366 1 NA NA 10.700983
30 NA NA 1.7556084 1 NA NA 10.700983
31 NA NA 1.9379339 1 NA NA 10.700983
32 NA NA 2.1391944 1 NA NA 10.770800
33 NA NA 2.3613565 1 NA NA 10.770800
34 NA NA 2.6065908 1 NA NA 15.826785
35 NA NA 2.8772934 1 NA NA 15.826785
36 NA NA 3.1761094 1 NA NA 17.202779
37 NA NA 3.5059583 1 NA NA 17.501642
38 NA NA 3.8700631 1 NA NA 17.501642
39 NA NA 4.2719813 1 NA NA 18.004036
40 NA NA 4.7156400 1 NA NA 18.018450
41 NA NA 5.2053741 1 NA NA 18.064443
42 NA NA 5.7459685 1 NA NA 18.203466
43 NA NA 6.3427054 1 NA NA 18.203466
44 NA NA 7.0014153 1 NA NA 18.207380
45 NA NA 7.7285343 1 NA NA 18.652771
46 NA NA 8.5311669 1 NA NA 18.652771
47 NA NA 9.4171554 1 NA NA 18.742123
48 NA NA 10.3951565 1 NA NA 18.974916
49 NA NA 11.4747262 1 NA NA 20.393352
50 NA NA 12.6664126 1 NA NA 21.257992
51 NA NA 13.9818594 1 NA NA 21.559807
52 NA NA 15.4339194 1 NA NA 23.204052
53 NA NA 17.0367805 1 NA NA 23.622406
54 NA NA 18.8061037 1 NA NA 24.602910
55 NA NA 20.7591766 1 NA NA 24.631676
56 NA NA 22.9150824 1 NA NA 24.839198
57 NA NA 25.2948857 1 NA NA 25.033974
58 NA NA 27.9218391 1 NA NA 25.156057
59 NA NA 30.8216098 1 NA NA 27.012538
60 NA NA 34.0225309 1 NA NA 27.071318
61 NA NA 37.5558777 1 NA NA 27.819910
62 NA NA 41.4561736 1 NA NA 27.819910
63 NA NA 45.7615276 1 NA NA 28.451458
64 NA NA 50.5140060 1 NA NA 28.704582
65 NA NA 55.7600443 1 NA NA 28.704582
66 NA NA 61.5509002 1 NA NA 28.708993
67 NA NA 67.9431546 1 NA NA 29.131892
68 NA NA 74.9992648 1 NA NA 29.322478
69 NA NA 82.7881742 1 NA NA 29.381832
70 NA NA 91.3859863 1 NA NA 29.423220
71 NA NA 100.8767082 1 NA NA 29.424055
72 NA NA 111.3530714 1 NA NA 29.424055
73 NA NA 122.9174379 1 NA NA 29.506052
74 NA NA 135.6828001 1 NA NA 29.534548
75 NA NA 149.7738854 1 NA NA 29.683823
76 NA NA 165.3283741 1 NA NA 29.683823
77 NA NA 182.4982454 1 NA NA 29.683823
78 NA NA 201.4512618 1 NA NA 29.683823
79 NA NA 222.3726086 1 NA NA 29.683823
80 NA NA 245.4667029 1 NA NA 29.683823
81 NA NA 270.9591915 1 NA NA 29.683823
82 NA NA 299.0991552 1 NA NA 29.683823
83 NA NA 330.1615426 1 NA NA 29.683823
84 NA NA 364.4498566 1 NA NA 29.683823
85 NA NA 402.2991197 1 NA NA 29.683823
86 NA NA 444.0791477 1 NA NA 29.683823
87 NA NA 490.1981630 1 NA NA 29.683823
88 NA NA 541.1067830 1 NA NA 29.683823
89 NA NA 597.3024232 1 NA NA 29.683823
90 NA NA 659.3341572 1 NA NA 29.683823
91 NA NA 727.8080818 1 NA NA 29.683823
92 NA NA 803.3932387 1 NA NA 29.683823
93 NA NA 886.8281517 1 NA NA 29.683823
94 NA NA 978.9280426 1 NA NA 29.683823
95 NA NA 1080.5927968 1 NA NA 29.683823
96 NA NA 1192.8157551 1 NA NA 29.683823
97 NA NA 1316.6934205 1 NA NA 29.683823
98 NA NA 1453.4361707 1 NA NA 29.683823
99 NA NA 1604.3800854 1 NA NA 29.683823
100 NA NA 1771.0000000 1 NA NA 29.683823
101 NA NA 0.1000000 2 NA NA 9.167934
102 NA NA 0.1103853 2 NA NA 9.167934
103 NA NA 0.1218492 2 NA NA 9.167934
104 NA NA 0.1345036 2 NA NA 9.167934
105 NA NA 0.1484722 2 NA NA 9.167934
106 NA NA 0.1638915 2 NA NA 9.167934
107 NA NA 0.1809122 2 NA NA 9.167934
108 NA NA 0.1997005 2 NA NA 9.167934
109 NA NA 0.2204400 2 NA NA 9.167934
110 NA NA 0.2433334 2 NA NA 9.167934
111 NA NA 0.2686043 2 NA NA 9.167934
112 NA NA 0.2964997 2 NA NA 9.167934
113 NA NA 0.3272921 2 NA NA 9.167934
114 NA NA 0.3612825 2 NA NA 9.167934
115 NA NA 0.3988028 2 NA NA 9.167934
116 NA NA 0.4402197 2 NA NA 9.167934
117 NA NA 0.4859379 2 NA NA 9.167934
118 NA NA 0.5364041 2 NA NA 9.167934
119 NA NA 0.5921113 2 NA NA 9.167934
120 NA NA 0.6536040 2 NA NA 9.167934
121 NA NA 0.7214828 2 NA NA 9.167934
122 NA NA 0.7964110 2 NA NA 9.167934
123 NA NA 0.8791208 2 NA NA 9.167934
124 NA NA 0.9704203 2 NA NA 9.167934
125 NA NA 1.0712015 2 NA NA 9.167934
126 NA NA 1.1824491 2 NA NA 9.167934
127 NA NA 1.3052502 2 NA NA 9.167934
128 NA NA 1.4408045 2 NA NA 9.167934
129 NA NA 1.5904366 2 NA NA 10.428882
130 NA NA 1.7556084 2 NA NA 10.428882
131 NA NA 1.9379339 2 NA NA 10.428882
132 NA NA 2.1391944 2 NA NA 10.484065
133 NA NA 2.3613565 2 NA NA 10.484065
134 NA NA 2.6065908 2 NA NA 14.723795
135 NA NA 2.8772934 2 NA NA 14.723795
136 NA NA 3.1761094 2 NA NA 15.959812
137 NA NA 3.5059583 2 NA NA 16.224111
138 NA NA 3.8700631 2 NA NA 16.224111
139 NA NA 4.2719813 2 NA NA 16.626122
140 NA NA 4.7156400 2 NA NA 16.643741
141 NA NA 5.2053741 2 NA NA 16.663846
142 NA NA 5.7459685 2 NA NA 16.757942
143 NA NA 6.3427054 2 NA NA 16.757942
144 NA NA 7.0014153 2 NA NA 16.757942
145 NA NA 7.7285343 2 NA NA 17.061307
146 NA NA 8.5311669 2 NA NA 17.061307
147 NA NA 9.4171554 2 NA NA 17.114256
148 NA NA 10.3951565 2 NA NA 17.239329
149 NA NA 11.4747262 2 NA NA 18.554618
150 NA NA 12.6664126 2 NA NA 19.310278
151 NA NA 13.9818594 2 NA NA 19.587296
152 NA NA 15.4339194 2 NA NA 21.733466
153 NA NA 17.0367805 2 NA NA 22.282012
154 NA NA 18.8061037 2 NA NA 23.640438
155 NA NA 20.7591766 2 NA NA 23.670278
156 NA NA 22.9150824 2 NA NA 23.956525
157 NA NA 25.2948857 2 NA NA 24.198335
158 NA NA 27.9218391 2 NA NA 24.362590
159 NA NA 30.8216098 2 NA NA 26.714680
160 NA NA 34.0225309 2 NA NA 26.790739
161 NA NA 37.5558777 2 NA NA 27.711281
162 NA NA 41.4561736 2 NA NA 27.711281
163 NA NA 45.7615276 2 NA NA 28.337999
164 NA NA 50.5140060 2 NA NA 28.580568
165 NA NA 55.7600443 2 NA NA 28.580568
166 NA NA 61.5509002 2 NA NA 28.606487
167 NA NA 67.9431546 2 NA NA 29.133397
168 NA NA 74.9992648 2 NA NA 29.323569
169 NA NA 82.7881742 2 NA NA 29.377291
170 NA NA 91.3859863 2 NA NA 29.398434
171 NA NA 100.8767082 2 NA NA 29.399269
172 NA NA 111.3530714 2 NA NA 29.399269
173 NA NA 122.9174379 2 NA NA 29.458148
174 NA NA 135.6828001 2 NA NA 29.477506
175 NA NA 149.7738854 2 NA NA 29.573336
176 NA NA 165.3283741 2 NA NA 29.573336
177 NA NA 182.4982454 2 NA NA 29.573336
178 NA NA 201.4512618 2 NA NA 29.573336
179 NA NA 222.3726086 2 NA NA 29.573336
180 NA NA 245.4667029 2 NA NA 29.573336
181 NA NA 270.9591915 2 NA NA 29.573336
182 NA NA 299.0991552 2 NA NA 29.573336
183 NA NA 330.1615426 2 NA NA 29.573336
184 NA NA 364.4498566 2 NA NA 29.573336
185 NA NA 402.2991197 2 NA NA 29.573336
186 NA NA 444.0791477 2 NA NA 29.573336
187 NA NA 490.1981630 2 NA NA 29.573336
188 NA NA 541.1067830 2 NA NA 29.573336
189 NA NA 597.3024232 2 NA NA 29.573336
190 NA NA 659.3341572 2 NA NA 29.573336
191 NA NA 727.8080818 2 NA NA 29.573336
192 NA NA 803.3932387 2 NA NA 29.573336
193 NA NA 886.8281517 2 NA NA 29.573336
194 NA NA 978.9280426 2 NA NA 29.573336
195 NA NA 1080.5927968 2 NA NA 29.573336
196 NA NA 1192.8157551 2 NA NA 29.573336
197 NA NA 1316.6934205 2 NA NA 29.573336
198 NA NA 1453.4361707 2 NA NA 29.573336
199 NA NA 1604.3800854 2 NA NA 29.573336
200 NA NA 1771.0000000 2 NA NA 29.573336
201 NA NA 0.1000000 3 NA NA 10.112622
202 NA NA 0.1103853 3 NA NA 10.112622
203 NA NA 0.1218492 3 NA NA 10.112622
204 NA NA 0.1345036 3 NA NA 10.112622
205 NA NA 0.1484722 3 NA NA 10.112622
206 NA NA 0.1638915 3 NA NA 10.112622
207 NA NA 0.1809122 3 NA NA 10.112622
208 NA NA 0.1997005 3 NA NA 10.112622
209 NA NA 0.2204400 3 NA NA 10.112622
210 NA NA 0.2433334 3 NA NA 10.112622
211 NA NA 0.2686043 3 NA NA 10.112622
212 NA NA 0.2964997 3 NA NA 10.112622
213 NA NA 0.3272921 3 NA NA 10.112622
214 NA NA 0.3612825 3 NA NA 10.112622
215 NA NA 0.3988028 3 NA NA 10.112622
216 NA NA 0.4402197 3 NA NA 10.112622
217 NA NA 0.4859379 3 NA NA 10.112622
218 NA NA 0.5364041 3 NA NA 10.112622
219 NA NA 0.5921113 3 NA NA 10.112622
220 NA NA 0.6536040 3 NA NA 10.112622
221 NA NA 0.7214828 3 NA NA 10.112622
222 NA NA 0.7964110 3 NA NA 10.112622
223 NA NA 0.8791208 3 NA NA 10.112622
224 NA NA 0.9704203 3 NA NA 10.112622
225 NA NA 1.0712015 3 NA NA 10.112622
226 NA NA 1.1824491 3 NA NA 10.112622
227 NA NA 1.3052502 3 NA NA 10.112622
228 NA NA 1.4408045 3 NA NA 10.112622
229 NA NA 1.5904366 3 NA NA 11.594290
230 NA NA 1.7556084 3 NA NA 11.594290
231 NA NA 1.9379339 3 NA NA 11.594290
232 NA NA 2.1391944 3 NA NA 11.666625
233 NA NA 2.3613565 3 NA NA 11.666625
234 NA NA 2.6065908 3 NA NA 16.730515
235 NA NA 2.8772934 3 NA NA 16.730515
236 NA NA 3.1761094 3 NA NA 18.069010
237 NA NA 3.5059583 3 NA NA 18.315577
238 NA NA 3.8700631 3 NA NA 18.315577
239 NA NA 4.2719813 3 NA NA 18.764906
240 NA NA 4.7156400 3 NA NA 18.771247
241 NA NA 5.2053741 3 NA NA 18.772272
242 NA NA 5.7459685 3 NA NA 18.881026
243 NA NA 6.3427054 3 NA NA 18.881026
244 NA NA 7.0014153 3 NA NA 18.881026
245 NA NA 7.7285343 3 NA NA 19.299718
246 NA NA 8.5311669 3 NA NA 19.299718
247 NA NA 9.4171554 3 NA NA 19.391513
248 NA NA 10.3951565 3 NA NA 19.569216
249 NA NA 11.4747262 3 NA NA 21.113427
250 NA NA 12.6664126 3 NA NA 22.076105
251 NA NA 13.9818594 3 NA NA 22.414190
252 NA NA 15.4339194 3 NA NA 24.251388
253 NA NA 17.0367805 3 NA NA 24.697859
254 NA NA 18.8061037 3 NA NA 25.663287
255 NA NA 20.7591766 3 NA NA 25.689034
256 NA NA 22.9150824 3 NA NA 25.905849
257 NA NA 25.2948857 3 NA NA 26.102714
258 NA NA 27.9218391 3 NA NA 26.227871
259 NA NA 30.8216098 3 NA NA 27.930820
260 NA NA 34.0225309 3 NA NA 27.953703
261 NA NA 37.5558777 3 NA NA 28.562051
262 NA NA 41.4561736 3 NA NA 28.562051
263 NA NA 45.7615276 3 NA NA 29.085419
264 NA NA 50.5140060 3 NA NA 29.321208
265 NA NA 55.7600443 3 NA NA 29.321208
266 NA NA 61.5509002 3 NA NA 29.320469
267 NA NA 67.9431546 3 NA NA 29.696444
268 NA NA 74.9992648 3 NA NA 29.880596
269 NA NA 82.7881742 3 NA NA 29.931594
270 NA NA 91.3859863 3 NA NA 29.954917
271 NA NA 100.8767082 3 NA NA 29.955752
272 NA NA 111.3530714 3 NA NA 29.955752
273 NA NA 122.9174379 3 NA NA 30.015219
274 NA NA 135.6828001 3 NA NA 30.036409
275 NA NA 149.7738854 3 NA NA 30.131526
276 NA NA 165.3283741 3 NA NA 30.131526
277 NA NA 182.4982454 3 NA NA 30.131526
278 NA NA 201.4512618 3 NA NA 30.131526
279 NA NA 222.3726086 3 NA NA 30.131526
280 NA NA 245.4667029 3 NA NA 30.131526
281 NA NA 270.9591915 3 NA NA 30.131526
282 NA NA 299.0991552 3 NA NA 30.131526
283 NA NA 330.1615426 3 NA NA 30.131526
284 NA NA 364.4498566 3 NA NA 30.131526
285 NA NA 402.2991197 3 NA NA 30.131526
286 NA NA 444.0791477 3 NA NA 30.131526
287 NA NA 490.1981630 3 NA NA 30.131526
288 NA NA 541.1067830 3 NA NA 30.131526
289 NA NA 597.3024232 3 NA NA 30.131526
290 NA NA 659.3341572 3 NA NA 30.131526
291 NA NA 727.8080818 3 NA NA 30.131526
292 NA NA 803.3932387 3 NA NA 30.131526
293 NA NA 886.8281517 3 NA NA 30.131526
294 NA NA 978.9280426 3 NA NA 30.131526
295 NA NA 1080.5927968 3 NA NA 30.131526
296 NA NA 1192.8157551 3 NA NA 30.131526
297 NA NA 1316.6934205 3 NA NA 30.131526
298 NA NA 1453.4361707 3 NA NA 30.131526
299 NA NA 1604.3800854 3 NA NA 30.131526
300 NA NA 1771.0000000 3 NA NA 30.131526
301 NA NA 0.1000000 4 NA NA 8.428925
302 NA NA 0.1103853 4 NA NA 8.428925
303 NA NA 0.1218492 4 NA NA 8.428925
304 NA NA 0.1345036 4 NA NA 8.428925
305 NA NA 0.1484722 4 NA NA 8.428925
306 NA NA 0.1638915 4 NA NA 8.428925
307 NA NA 0.1809122 4 NA NA 8.428925
308 NA NA 0.1997005 4 NA NA 8.428925
309 NA NA 0.2204400 4 NA NA 8.428925
310 NA NA 0.2433334 4 NA NA 8.428925
311 NA NA 0.2686043 4 NA NA 8.428925
312 NA NA 0.2964997 4 NA NA 8.428925
313 NA NA 0.3272921 4 NA NA 8.428925
314 NA NA 0.3612825 4 NA NA 8.428925
315 NA NA 0.3988028 4 NA NA 8.428925
316 NA NA 0.4402197 4 NA NA 8.428925
317 NA NA 0.4859379 4 NA NA 8.428925
318 NA NA 0.5364041 4 NA NA 8.428925
319 NA NA 0.5921113 4 NA NA 8.428925
320 NA NA 0.6536040 4 NA NA 8.428925
321 NA NA 0.7214828 4 NA NA 8.428925
322 NA NA 0.7964110 4 NA NA 8.428925
323 NA NA 0.8791208 4 NA NA 8.428925
324 NA NA 0.9704203 4 NA NA 8.428925
325 NA NA 1.0712015 4 NA NA 8.428925
326 NA NA 1.1824491 4 NA NA 8.428925
327 NA NA 1.3052502 4 NA NA 8.428925
328 NA NA 1.4408045 4 NA NA 8.428925
329 NA NA 1.5904366 4 NA NA 10.026569
330 NA NA 1.7556084 4 NA NA 10.026569
331 NA NA 1.9379339 4 NA NA 10.026569
332 NA NA 2.1391944 4 NA NA 10.097620
333 NA NA 2.3613565 4 NA NA 10.097620
334 NA NA 2.6065908 4 NA NA 15.223820
335 NA NA 2.8772934 4 NA NA 15.223820
336 NA NA 3.1761094 4 NA NA 16.663703
337 NA NA 3.5059583 4 NA NA 16.986115
338 NA NA 3.8700631 4 NA NA 16.986115
339 NA NA 4.2719813 4 NA NA 17.538289
340 NA NA 4.7156400 4 NA NA 17.576236
341 NA NA 5.2053741 4 NA NA 17.624137
342 NA NA 5.7459685 4 NA NA 17.856198
343 NA NA 6.3427054 4 NA NA 17.856198
344 NA NA 7.0014153 4 NA NA 17.860112
345 NA NA 7.7285343 4 NA NA 18.384132
346 NA NA 8.5311669 4 NA NA 18.384132
347 NA NA 9.4171554 4 NA NA 18.506240
348 NA NA 10.3951565 4 NA NA 18.793446
349 NA NA 11.4747262 4 NA NA 20.196619
350 NA NA 12.6664126 4 NA NA 21.231373
351 NA NA 13.9818594 4 NA NA 21.545542
352 NA NA 15.4339194 4 NA NA 22.932070
353 NA NA 17.0367805 4 NA NA 23.278689
354 NA NA 18.8061037 4 NA NA 24.202492
355 NA NA 20.7591766 4 NA NA 24.221923
356 NA NA 22.9150824 4 NA NA 24.418336
357 NA NA 25.2948857 4 NA NA 24.600524
358 NA NA 27.9218391 4 NA NA 24.721067
359 NA NA 30.8216098 4 NA NA 26.393707
360 NA NA 34.0225309 4 NA NA 26.424651
361 NA NA 37.5558777 4 NA NA 27.052639
362 NA NA 41.4561736 4 NA NA 27.052639
363 NA NA 45.7615276 4 NA NA 27.598854
364 NA NA 50.5140060 4 NA NA 27.832015
365 NA NA 55.7600443 4 NA NA 27.832015
366 NA NA 61.5509002 4 NA NA 27.841674
367 NA NA 67.9431546 4 NA NA 28.207443
368 NA NA 74.9992648 4 NA NA 28.378639
369 NA NA 82.7881742 4 NA NA 28.430997
370 NA NA 91.3859863 4 NA NA 28.460565
371 NA NA 100.8767082 4 NA NA 28.461399
372 NA NA 111.3530714 4 NA NA 28.461399
373 NA NA 122.9174379 4 NA NA 28.522180
374 NA NA 135.6828001 4 NA NA 28.544542
375 NA NA 149.7738854 4 NA NA 28.649531
376 NA NA 165.3283741 4 NA NA 28.649531
377 NA NA 182.4982454 4 NA NA 28.649531
378 NA NA 201.4512618 4 NA NA 28.649531
379 NA NA 222.3726086 4 NA NA 28.649531
380 NA NA 245.4667029 4 NA NA 28.649531
381 NA NA 270.9591915 4 NA NA 28.649531
382 NA NA 299.0991552 4 NA NA 28.649531
383 NA NA 330.1615426 4 NA NA 28.649531
384 NA NA 364.4498566 4 NA NA 28.649531
385 NA NA 402.2991197 4 NA NA 28.649531
386 NA NA 444.0791477 4 NA NA 28.649531
387 NA NA 490.1981630 4 NA NA 28.649531
388 NA NA 541.1067830 4 NA NA 28.649531
389 NA NA 597.3024232 4 NA NA 28.649531
390 NA NA 659.3341572 4 NA NA 28.649531
391 NA NA 727.8080818 4 NA NA 28.649531
392 NA NA 803.3932387 4 NA NA 28.649531
393 NA NA 886.8281517 4 NA NA 28.649531
394 NA NA 978.9280426 4 NA NA 28.649531
395 NA NA 1080.5927968 4 NA NA 28.649531
396 NA NA 1192.8157551 4 NA NA 28.649531
397 NA NA 1316.6934205 4 NA NA 28.649531
398 NA NA 1453.4361707 4 NA NA 28.649531
399 NA NA 1604.3800854 4 NA NA 28.649531
400 NA NA 1771.0000000 4 NA NA 28.649531
401 NA NA 0.1000000 5 NA NA 6.999531
402 NA NA 0.1103853 5 NA NA 6.999531
403 NA NA 0.1218492 5 NA NA 6.999531
404 NA NA 0.1345036 5 NA NA 6.999531
405 NA NA 0.1484722 5 NA NA 6.999531
406 NA NA 0.1638915 5 NA NA 6.999531
407 NA NA 0.1809122 5 NA NA 6.999531
408 NA NA 0.1997005 5 NA NA 6.999531
409 NA NA 0.2204400 5 NA NA 6.999531
410 NA NA 0.2433334 5 NA NA 6.999531
411 NA NA 0.2686043 5 NA NA 6.999531
412 NA NA 0.2964997 5 NA NA 6.999531
413 NA NA 0.3272921 5 NA NA 6.999531
414 NA NA 0.3612825 5 NA NA 6.999531
415 NA NA 0.3988028 5 NA NA 6.999531
416 NA NA 0.4402197 5 NA NA 6.999531
417 NA NA 0.4859379 5 NA NA 6.999531
418 NA NA 0.5364041 5 NA NA 6.999531
419 NA NA 0.5921113 5 NA NA 6.999531
420 NA NA 0.6536040 5 NA NA 6.999531
421 NA NA 0.7214828 5 NA NA 6.999531
422 NA NA 0.7964110 5 NA NA 6.999531
423 NA NA 0.8791208 5 NA NA 6.999531
424 NA NA 0.9704203 5 NA NA 6.999531
425 NA NA 1.0712015 5 NA NA 6.999531
426 NA NA 1.1824491 5 NA NA 6.999531
427 NA NA 1.3052502 5 NA NA 6.999531
428 NA NA 1.4408045 5 NA NA 6.999531
429 NA NA 1.5904366 5 NA NA 8.242485
430 NA NA 1.7556084 5 NA NA 8.242485
431 NA NA 1.9379339 5 NA NA 8.242485
432 NA NA 2.1391944 5 NA NA 8.299944
433 NA NA 2.3613565 5 NA NA 8.299944
434 NA NA 2.6065908 5 NA NA 12.891059
435 NA NA 2.8772934 5 NA NA 12.891059
436 NA NA 3.1761094 5 NA NA 14.190581
437 NA NA 3.5059583 5 NA NA 14.480571
438 NA NA 3.8700631 5 NA NA 14.480571
439 NA NA 4.2719813 5 NA NA 14.958219
440 NA NA 4.7156400 5 NA NA 14.994170
441 NA NA 5.2053741 5 NA NA 14.998897
442 NA NA 5.7459685 5 NA NA 15.185881
443 NA NA 6.3427054 5 NA NA 15.185881
444 NA NA 7.0014153 5 NA NA 15.188343
445 NA NA 7.7285343 5 NA NA 15.532640
446 NA NA 8.5311669 5 NA NA 15.532640
447 NA NA 9.4171554 5 NA NA 15.604671
448 NA NA 10.3951565 5 NA NA 15.763563
449 NA NA 11.4747262 5 NA NA 17.104393
450 NA NA 12.6664126 5 NA NA 17.750604
451 NA NA 13.9818594 5 NA NA 17.984302
452 NA NA 15.4339194 5 NA NA 19.399744
453 NA NA 17.0367805 5 NA NA 19.744986
454 NA NA 18.8061037 5 NA NA 21.325005
455 NA NA 20.7591766 5 NA NA 21.340849
456 NA NA 22.9150824 5 NA NA 21.592203
457 NA NA 25.2948857 5 NA NA 21.856382
458 NA NA 27.9218391 5 NA NA 22.009137
459 NA NA 30.8216098 5 NA NA 24.054173
460 NA NA 34.0225309 5 NA NA 24.101170
461 NA NA 37.5558777 5 NA NA 24.736093
462 NA NA 41.4561736 5 NA NA 24.736093
463 NA NA 45.7615276 5 NA NA 25.218335
464 NA NA 50.5140060 5 NA NA 25.420046
465 NA NA 55.7600443 5 NA NA 25.420046
466 NA NA 61.5509002 5 NA NA 25.433817
467 NA NA 67.9431546 5 NA NA 25.809951
468 NA NA 74.9992648 5 NA NA 25.974738
469 NA NA 82.7881742 5 NA NA 26.027097
470 NA NA 91.3859863 5 NA NA 26.045023
471 NA NA 100.8767082 5 NA NA 26.045858
472 NA NA 111.3530714 5 NA NA 26.045858
473 NA NA 122.9174379 5 NA NA 26.100690
474 NA NA 135.6828001 5 NA NA 26.112327
475 NA NA 149.7738854 5 NA NA 26.194113
476 NA NA 165.3283741 5 NA NA 26.194113
477 NA NA 182.4982454 5 NA NA 26.194113
478 NA NA 201.4512618 5 NA NA 26.194113
479 NA NA 222.3726086 5 NA NA 26.194113
480 NA NA 245.4667029 5 NA NA 26.194113
481 NA NA 270.9591915 5 NA NA 26.194113
482 NA NA 299.0991552 5 NA NA 26.194113
483 NA NA 330.1615426 5 NA NA 26.194113
484 NA NA 364.4498566 5 NA NA 26.194113
485 NA NA 402.2991197 5 NA NA 26.194113
486 NA NA 444.0791477 5 NA NA 26.194113
487 NA NA 490.1981630 5 NA NA 26.194113
488 NA NA 541.1067830 5 NA NA 26.194113
489 NA NA 597.3024232 5 NA NA 26.194113
490 NA NA 659.3341572 5 NA NA 26.194113
491 NA NA 727.8080818 5 NA NA 26.194113
492 NA NA 803.3932387 5 NA NA 26.194113
493 NA NA 886.8281517 5 NA NA 26.194113
494 NA NA 978.9280426 5 NA NA 26.194113
495 NA NA 1080.5927968 5 NA NA 26.194113
496 NA NA 1192.8157551 5 NA NA 26.194113
497 NA NA 1316.6934205 5 NA NA 26.194113
498 NA NA 1453.4361707 5 NA NA 26.194113
499 NA NA 1604.3800854 5 NA NA 26.194113
500 NA NA 1771.0000000 5 NA NA 26.194113loyn.fit <-
loyn.boot |>
dplyr::select(Boot, fit) |>
unnest(fit) |>
group_by(AREA, fGRAZE) |>
ggdist::median_hdci(fit)
g1 <- loyn.fit |> ggplot(aes(y = fit, x = AREA, fill = fGRAZE, color = fGRAZE)) +
geom_ribbon(aes(ymin = .lower, ymax = .upper), alpha = 0.3, color = NA) +
geom_line() +
scale_fill_viridis_d() +
scale_colour_viridis_d() +
scale_x_log10() +
theme_classic()
loyn.infl <-
loyn.boot |>
dplyr::select(Boot, infl) |>
unnest(infl) |>
group_by(var) |>
ggdist::median_hdci(rel.inf)
g2 <- loyn.inf |>
arrange(rel.inf) |>
mutate(var = factor(var, levels = unique(var))) |>
ggplot(aes(y = var, x = rel.inf)) +
geom_vline(xintercept = 12.5, linetype = "dashed") +
geom_pointrange(aes(xmin = .lower, xmax = .upper)) +
theme_classic()
g2 + patchwork::inset_element(g1, left = 0.3, bottom = 0.01, right = 1, top = 0.7)
library(randomForest)
loyn.rf <- randomForest(ABUND ~ DIST + LDIST + AREA + fGRAZE + ALT + YR.ISOL,
data = loyn, importance = TRUE,
ntree = 1000
)
loyn.imp <- randomForest::importance(loyn.rf)
## Rank by either:
## *MSE (mean decrease in accuracy)
## For each tree, calculate OOB prediction error.
## This also done after permuting predictors.
## Then average diff of prediction errors for each tree
## *NodePurity (mean decrease in node impurity)
## Measure of the total decline of impurity due to each
## predictor averaged over trees
100 * loyn.imp / sum(loyn.imp) %IncMSE IncNodePurity
DIST -0.081225849 6.437963
LDIST -0.001620151 7.087230
AREA 0.602557933 36.341377
fGRAZE 0.391291859 22.330945
ALT 0.109146005 9.226453
YR.ISOL 0.252253722 17.303628
11 References
Loyn, R. H. 1987. “Nature Conservation: The Role of Remnants of Native Vegetation.” In, edited by D. A. Saunders, G. W. Arnold, A. A. Burbridge, and A. J. M. Hopkins. Chipping Norton, NSW: Surrey Beatty & Sons.